Question

In: Math

Ordinary Differential equation (Newton's Law)

An object is thrown vertically upward from the ground with an initial velocity of 1960 cm/s. neglecting air resistance, find a) the maximum height reached, and b) the total time is taken to return to the starting point.

Solutions

Expert Solution

by using Newton's Law, we can get the actual answer for this problem. The final velocity is 0 because it reached on the top height and no movement, make the ground as the initial part. 

Acceleration of the object when it downward must be in (negative) because the gravitational of the object move downward which is opposite.

use the Newton's Law to solve this ODE problem (netforce=weight)

Azmir Tamim answered 3 years ago
Next > < Previous

Related Solutions

differential equation 12. Newton's law of cooling states that the temperature of an object changes at...
differential equation 12. Newton's law of cooling states that the temperature of an object changes at a rate pro-portional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 200F when freshly poured, and 1 min later has cooled to 190F in a room at 70F, determine when the coffee reaches a temperature of 150F.
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (1-x)y"+xy-y=0, x0=0
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (4-x2)y"+2y=0, x0
1. Give an example of a 3rd order nonlinear ordinary differential equation.
1. Give an example of a 3rd order nonlinear ordinary differential equation.
some people describe Newton's second law as a quantitative version of Newton's first law . Describe...
some people describe Newton's second law as a quantitative version of Newton's first law . Describe how this makes sense.
Ordinary Differential Equations
The rate at which the ice melts is proportional to the amount of ice at the instant. Find the amount of ice left after 2 hours if half the quantity melts in 30 minutes. Solution. Let m be the amount of ice at any time t.
Ordinary Differential Equations
Solve the following problems. \( \frac{d y}{d t} \tan y=\sin (t+y)+\sin (t+y) \)  
Ordinary Differential Equations
Solve the following problems. (a) \( \frac{d y}{d t}=2+\frac{y}{t} \) (b)  \( 3 t+2 y \frac{d y}{d t}=y \)
Ordinary Differential Equations
Solve the following problems.      \( t y \frac{d y}{d t}=\sqrt{t^{2} y^{2}+t^{2}+y^{2}+1} \)
Ordinary Differential Equations
Write a differential equation in wich \( y^2=4(t+1) \) is a solutiion.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT